I have a simple question (I hope I can explain it clear enough). I want to train and apply a PCA to a set of data (I want to have an orthogonal basis in a low dimension subspace with unitary vectors), but the criteria that I want to maximize for the projected axes is not the variance of the data.
I was wondering if using the eigenvectors of a symmetric matrix other than the covariance matrix still gives a correct and usable basis.
For example: Let's say I have a symmetric matrix that represents a certain distance on each dimension computed over my data. Does the first eigen-vector of that matrix represent an axis that maximizes that distance ? And could the whole set of eigenvectors be used as basis ?
Sorry if the question is silly, but any response will be of big help. Thanks !